You don't have to bring your own corkscrew - ask your cabin steward to get one for you.
To me that's tacky, taking your wine in a glass to the dining room. HAL has been very lenient in allowing us to bring our own wine on board for consumpation in our cabin, but if everyone did what you suggest then there's a good chance that one day HAL will ban wine/champagne/soda like they do hard liquour and beer.
As for bringing it from home wrapped in towels, you are taking a chance - have you seen they way the baggage handlers handle the luggage at Pearson and on the ship. You may be lucky and nothing breaks but if it does, then you'll have to wash everything in your suitcase. Many years ago we were with a couple from Kitchener and they did this - oh, boy did their clothes reek until they could wash/get them cleaned !!
I'd get the cab to stop at a liquour store in FLL on the way to the ship. I believe there are a couple of big stores on the way to the ship. Either the cabbie will know where they are or someone on this board will know the name of them.
As far as I know no liquour stores in T&C but probably a few nearby in PC.
Good luck and have a GREAT CRUISE. We did this cruise on the EUDM in December and will probably do it again at Xmas.